THE DIVIDE-AND-CONQUER SEQUENTIAL MONTE CARLO ALGORITHM: THEORETICAL PROPERTIES AND LIMIT THEOREMS

• 成果类型: Article
• 署名作者: Kuntz, Juan; Crucinio, Francesca R.; Johansen, Adam M.
• 署名单位: University of Warwick; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1996
• 发表日期: 2024
• 页码: 1469-1523
• 关键词: particle filter; CONVERGENCE

摘要

We provide a comprehensive characterisation of the theoretical properties of the divide-and-conquer sequential Monte Carlo (DaC-SMC) algorithm. We firmly establish it as a well-founded method by showing that it possesses the same basic properties as conventional sequential Monte Carlo (SMC) algorithms do. In particular, we derive pertinent laws of large numbers, Lp inequalities, and central limit theorems; and we characterize the bias in the normalized estimates produced by the algorithm and argue the absence thereof in the unnormalized ones. We further consider its practical implementation and several interesting variants; obtain expressions for its globally and locally optimal intermediate targets, auxiliary measures, and proposal kernels; and show that, in comparable conditions, DaC-SMC proves more statistically efficient than its direct SMC analogue. We close the paper with a discussion of our results, open questions, and future research directions.